zbMATH — the first resource for mathematics

Bremmer series that correct parabolic approximations. (English) Zbl 0313.35020

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35C10 Series solutions to PDEs
35A35 Theoretical approximation in context of PDEs
Full Text: DOI
[1] Bremmer, H, The W.K.B approximation as a first term of a geometric-optical series, Commun. pure appl. math., 4, 105, (1951) · Zbl 0043.20301
[2] Fock, V.A, Electromagnetic diffraction and propagation problems, (1960), McMillian New York
[3] Bellman, R; Kalaba, R, Functional equations, wave propagation, and invariant imbedding, J. math. mech., 8, 683, (1959) · Zbl 0090.45301
[4] {\scJ. Corones and D. W. McLaughlin}, The Parabolic Approximation in Focusing Media, to appear.
[5] Sluijter, F.W, Generalizations of the bremmer series based on physical concepts, J. math. anal. appl., 27, 282-302, (1969) · Zbl 0176.47101
[6] Sluijter, F.W, Arbitrariness of dividing the total field in an optical inhomogenous medium into direct and reversed waves, J. opt. soc. am., 60, 8, (1970)
[7] Arnaud, J.A, Nonorthogonal waveguides and resonators, Bell syst. tech. J., 49, 2311, (1970) · Zbl 0213.11503
[8] Atkinson, F.V, Wave propagation and bremmer series, J. math. anal. appl., 1, 255, (1960) · Zbl 0103.05502
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.